irrationality

n. illogic, lack of reason, want of rational thought

For irrationality as it relates to numbers, see irrational number. Irrationality is talking or acting without regard of rationality. Usually pejorative, the term is used to describe thinking and actions which are, or appear to be, less useful or logical than the rational alternatives. There is a clear tendency to view our own thoughts, words, and actions as rational and to see those who disagree as irrational.
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Ir·ra·tion·al adj. Not rational; marked by a lack of accord with reason or sound judgment. irrational adjective Unreasonable, illogical [more]Irrationality - Community and Resources

Noun
1. the state of being irrational; lacking powers of understanding
(synonym) unreason
(hypernym) insanity

(n.)
The quality or state of being irrational.